Optimal Control of Second Order Sweeping Processes with Discrete and Differential Inclusions

Elimhan N. Mahmudov*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

3 Citations (Scopus)

Abstract

We discuss the problem of optimal control theory given by second order sweeping processes with discrete and differential inclusions. The main problem is to derive sufficient optimality conditions for second-order sweeping processes with differential inclusions. By using first and second order difference operators in a continuous problem we associate the second order sweeping processes with a discrete-approximate problem. On the basis of the discretization method in the form of Euler-Lagrange inclusions, optimality conditions for discrete approximate inclusions and transversality conditions are obtained. The establishment of Euler-Lagrange type adjoint inclusions is based on the presence of equivalence relations for locally adjoint mappings. To demonstrate the results obtained, a second-order sweeping process with a “linear” differential inclusion is considered.

Original languageEnglish
Pages (from-to)269-290
Number of pages22
JournalJournal of Convex Analysis
Volume29
Issue number1
Publication statusPublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 Heldermann Verlag. All rights reserved.

Keywords

  • adjoint mappings
  • approximation
  • Euler-Lagrange inclusions
  • second order
  • set-valued map
  • sweeping
  • transversality

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